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NPS-61Fr77101
UBRAflTTECHNICAL RFPCRT SECT1
NAVAL PC 'ATE S
MONTEREY. CALIFORNIA
NAVAL POSTGRADUATE SCHOOL
Monterey, California
ALTITUDE DEPENDENCE OF CT2OVER THE OCEAN
C. W. Fairall
and
Ralph Markson and Jan Sedlacek
1 October 1977
Approved for public release; distribution unlimited
spared for: Naval Air Systems Command
FEDDOCS Washington, D.C. 20360
D 208.14/2:NPS-61Fr77101
NAVAL POSTGRADUATE SCHOOLMonterey, California
Rear Admiral I. W. Linder J. R. BorstingSuperintendent Provost
The work reported herein was supported in part by the Naval Air SystemsCommand, Washington, D.C.
Reproduction of all or part of this report is authorized.
This report was prepared by:
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1. REPORT NUMBER
NPS-61Fr77101
2. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER
4. TITLE (and Subtitle)
Altitude Dependence of C- Over The Ocean
5. TYPE OF REPORT & PERIOD COVERED
Sep 1976 - Jun 1977
6. PERFORMING ORG. REPORT NUMBER
7. AUTHORS
C. W. Fairall, Ralph Markson and Jan Sedlacek
8. CONTRACT OR GRANT NUMBERfa;
NAVAIR N00019-76-C-0588and NAVSEA PMS 405
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Department of Physics § Chemistry-Naval Postgraduate SchoolMonterey, CA 93940
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Naval Air Systems CommandWashington, D.C. 20360
12. REPORT DATE
1 October 197713. NUMBER OF PAGES
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The height dependence of the temperature structure parameter, CT , has beenmeasured with microthermal sensors mounted on a light aircraft. This workwas done in conjunction with optical propagation and turbulent transportresearch in the marine boundary layer. These measurements indicate that,in the absence of a strong inversion, the constant stress layer can besurprisingly thin. The measurements also substantiate the strong role playedby temperature and water vapor discontinuities in turbulence above the boundarylaver
W 1 JAN 73 1473 EDITION OF 1 NOV 85 IS OBSOLETES/N 0102-014- 5601 |
UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE (When Data Bnierod)
ALTITUDE DEPENDENCE OF C^ OVER THE OCEAN
C. W. FairallEnvironmental Physics GroupNaval Postgraduate School
Monterey, CA 93940
and
Ralph Markson and Jan SedlacekAirborne Research Associates
46 Kendal Common RoadWeston, MA 02193
ABSTRACT
2The height dependence of the temperature structure parameter, C
'
has been measured with microthermal sensors mounted on a light air-
craft. This work was done in conjunction with optical propagation
and turbulent transport research in the marine boundary layer.
These measurements indicate that, in the absence of a strong inver-
sion, the constant stress layer can be surprisingly thin. The measure-
ments also substantiate the strong role played by temperature and water
vapor discontinuities in turbulence above the boundary layer.
ALTITUDE DEPENDENCE OF ATMOSPHERIC TURBULENCE OVER THE OCEAN
I
.
INTRODUCTION
A. General Comments
1. Optical propagation
2
.
Transport
B. Other Work
C. Operational Games
II. INSTRUMENTATION AND TECHNIQUES
A. Platform
1. Airplane
2
.
Other measurements
B. CT2
1
.
Two wire definition
2. Probes
3. Noise
III. THEORY
A. Boundary Layer
1. Define U*, T , R. , L
2. Expressions for C~3. Expected height dependence
B. Above Boundary Layer
1. Length scale2
2. C^
IV. RESULTS
A. Ship Results
B. Airplane
1. CEWCOM 76
2. NJ
3. HAYES 77
V. CONCLUSIONS 11
A. Boundary Layer
B. Above Boundary Layer
REFERENCES 13
FIGURE CAPTIONS 15
li
I . INTRODUCTION
2We have made measurements of temperature structure parameter, CL , from
a light aircraft using microthermal sensors as part of a study of turbulence
2in the marine boundary layer. CT
is important for optical propagation
studies due to its relation to the index of refraction structure parameter,
CN2
, [Friehe (1977)]
CN2
= (79 x 10"6P/T2)
2(CT2
+ .11 CL + 3.2 x 10" 3C
2) (1)
2where: C is the water vapor structure parameter,
CT is the cospectrum structure parameter,
p is the pressure in mb, and
T is the absolute temperature.
The water vapor fluctuations are usually relatively small so we can write
C^2
= (79 x 10"6P/T2)
2CT2
(2)
2 2This relationship is shown in Fig. 1 with C^ /CL, as a function of altitude
for the U.S. Standard Atmosphere. Turbulence is also of interest because of
the role of eddy diffusion in the transport of heat, water vapor, and pol-
lutants. These factors are important in the formation of marine fog and air
pollution modeling.
2Only a few measurements of the altitude dependence of CL, have been made
2to date. Korpov and Tsvang (1966) have made measurements of CL with an
acoustic anemometer on an airplane and have related their results to the
vertical temperature gradient. Microthermal sensors have been used to measure
2CL with balloon borne equipment by Bufton (1973) and airplane borne equipment
by Lawrence (1970) and Collins (1977) . Recently, Hanson (1976) has combined
airplane microthermal measurements and remote scintillometer determinations
2of C, and compared his results with an impirical model developed by Yura.
Based on this body of data, Hall (1977) has compiled a conglomerate curve
2of C_ as a function of altitude (Fig. 2) for daytime overland data. Only
Ochs (1973) has reported measurements over the ocean.
The data we are reporting on were taken as part of three separate
research operations . The first was the "Cooperative Experiment for West
Coast Oceanography and Meteorology - 1976" (designated CEWCOM 76) , a marine
fog research project off San Diego. CEWCOM 76 was organized by the Naval
Postgraduate School and the Naval Electronics Laboratory Center. The second
was a marine fog and aerosol project in the Gulf of Mexico off Panama City,
Florida (designated FLORIDA 77) . The third was in conjunction with a turbu-
lence and aerosol research cruise on the USNS Hayes in the Atlantic (desig-
nated HAYES 77) organized by the Naval Research Laboratory.
II. INSTRUMENTATION AND TECHNIQUES
The platform for our measurements is a single engine turbocharged
Bellanca operated by Airborne Research Associates (Fig. 3) . This aircraft
has been flown as low as 3 meters and as high as 10,000 meters and makes an
excellent tool for the low altitude flights required for boundary layer
research. The aircraft is well instrumented, allowing simultaneous measure-
ments of air temperature, altitude, dew point, electric field, visibility,
infrared surface temperature, and microwave refractive index. The data is
normally recorded with an eight channel strip chart recorder.
The temperature structure parameter is measured using the paired sensor
method. Given two temperature sensors, 1 and 2, a distance d apart, then
[Lumley (1964)]
CT2
= < (T2
- T:)
2> d'
2/3(3)
This quantity is related to the Kolmogorov power spectral density of tempera-
ture fluctuations, <j>T (k),
*T Ck) = .25 CT2
k~5/3
(4)
where k is the wave number. Equation 4 applies in the inertial subrange part
of the spectrum where the turbulence is nearly isotropic, allowing a one-
2dimensional representation of
<J>T (k) . C™ is independent of d in the inertial
subrange
.
2The device we have used to measure CL, is a DC Wheatstone bridge (Thermo
Systems Model 1044) that senses the relative resistance fluctuations of a
pair of 2.5 micron diameter platinum wires separated by about one meter.
The sensors were originally mounted on tne leading edge of the wing (CEW-
COM 76 and FLORIDA 77) but the noise level was very high so the sensors
were moved to the present wing tip location (Fig. 4) . The output of the
bridge (proportional to AT = T2
- T,) is processed by an RMS module with
a 5 sec time constant and recorded on the strip chart recorder as ATRMC.
.
The sensitivity is limited by the broad band noise of the system due to
inherent amplifier noise and pickup from the aircraft ignition system.
2 -4For CEWCOM 76 and FLORIDA 77 the noise level corresponds to L ~ 4 x 10
2 2/3 2 -4 2 2/3k /m , for HAYES 77 the noise level is lower (CL —
' 10 k /m ) since
we were using the wing tip probe configuration. It is possible to improve
the accuracy by correcting for the noise. If we assume an RMS noise level
of N, then the noise correction appears as
ct2
= c <AW 2- n2
i d" 2/3 &
Since 2.5 micron wires are fragile, breakage is a continual problem.
Except for one bad batch of wires, we have found a typical lifetime of one
or two flights for a given wire. We presently have two pairs of sensors
mounted and can switch to a good pair if one wire breaks
.
III. THEORY
The boundary layer is that part of the atmosphere where friction
with and heating by the surface play an important part in the generation
of turbulence. Near the surface the shear stress and scalar fluxes are
essentially constant. In this region the fluxes can be represented by
scaling parameters (such as U # and T*) that are independent of height.
We shall refer to this layer of nearly constant stress and flux as the
surface layer. In the surface layer, the height above the surface, Z,
is the appropriate turbulence length parameter. For a complete treatment
of the surface layer equations we suggest Lumely (1964) , Businger (1971)
or Kraus (1972) . The normalized momentum flux, F , and the normalized
heat flux, F, , for turbulent transport are
F = - < u'w 1 > = LL2
(6)m *
Fh
= - < T'w' > = U*T* (7)
where u' is the horizontal velocity fluctuations,
w" is the vertical velocity fluctuations,
T' is the temperature fluctuations,
U* is the friction velocity, and
T* is the scaling temperature.
The atmospheric stability is represented by either the Monin-Obukov length,
L, or the Richardson number, R.
,
l
2T U*
L wz (8)
g(3T/3Z)R.
V—j (9)
T(3U/3Z)
where T is the virtual potential temperature,
g is the acceleration of gravity,
U is the mean horizontal velocity, and
K = .35 is the Von Karmon constant.
The mean and fluctuating temperature dependences on height are given by
[Wyngaard (1971)]
T
I = kzfiw (10)
CT2
= T*2
Z_2/3
f2
(Z/L) (11)
Under near-neutral conditions f, and f?
are equal to unity, resulting in a
2 -2/3logarithmic mean temperature profile and CL proportional to Z '
. Under
2 -4/3unstable conditions (- Z/L » 1/7) CT is proportional to Z . These
relationships are based on measurements made on a flat Kansas plain with
averaging times of about one hour. Due to the shorter average time invol-
ved in aircraft profiles, one expects scatter about the curve of Eq. 11
even in the surface layer.
Wyngaard points out that although these results are based on surface
measurements (Z < 22 m) they are valid to somewhat greater heights. In
2the case of the well developed unstable boundary layer, the predicted CL,
profile is valid well beyond the surface layer. Although Davidson (1977)
has found evidence of wave influence restrictions on the lower limit of
the oceanic surface layer equations, the primary interest of optics and
transport users is in establishing the upper limits of validity.
The upper limit is often assumed to be at least half the distance
to the first inversion. This distinction becomes even more tenuous if
there is no low inversion. Above the surface layer, equations 10 and 11
become meaningless when defined in terms of the absolute height above the
surface, Z. Since the vertical gradients are still meaningful, Richardson
number remains a useful representation of stability. The appropriate
length parameter is the integral scale (or outer scale), A, which is a
measure of the largest size (or minimum wave number) for which the
Kolmogorov spectrum of equation 4 is valid [Hinze (1959)]. In the surface
layer A is proportional to Z . In this representation we have
I = Fat
fi (V ™
CT2
= T*2
(AT)~ 2/3
ff» (R.) (13)
where f,' and f ' are analogous to f. and £~
IV . RESULTS
2Shipboard and platform measurements of C_ have shown fairly good
agreement with the predicted height dependence in the near surface layer
(Z < 25 meters). Fig. 5 shows a profile taken at the Naval Coastal Systems
Laboratory's Stage I in the Gulf of Mexico during FLORIDA 77. We have
found the marine surface layer to be predominately near -neutral with a
tendency to be slightly unstable. Based on numerous shipboard measure-
ments we have found typical values of L: • 100 meters and T* r - .08 °C.
2Using these values we have indicated typical surface based CT profile
(from equation 11) as the dashed line in Fig. 2. Under these conditions
we would expect C„ ** Z to be a good approximation for Z > 20 meters.
However, during HAYES 77 we found the Atlantic Coast from Cape Code to
Newfoundland to have a stable surface layer. It has been our experience
from various shipboard operations that stable conditions are most likely
2to produce anomalous CT profiles in the near surface layer.
The surface layer is usually well defined off the Pacific Coast of
the United States due to the persistence of a strong marine inversion.
Consequently, we can expect CT to be well described by the Z or Z
2equation. In Fig. 6 we have two aircraft measurements of CT before and
after a radiosonde balloon launch during near neutral conditions. The
CT
profile is very well fit by the Z~ law until the inversion is
2reached, where CT increases rapidly with the temperature gradient. In
this case the surface layer dominates the entire boundary layer. The strong
2peak in CT
at the inversion (Z ~ 200 m) is in agreement with the ship's
acoustic sounder.
The Atlantic Coast data taken during HAYES 77 is considerably less
encouraging. In Fig. 7 we can see a well developed surface layer similar
to the Pacific Coast profile of Fig. 6. The marine inversion occurs at
Z = 200 meters. There is also a strong layer of turbulence which occurs
above a sharp temperature discontinuity at Z - 1700 meters. In Fig. 8
the well defined surface layer extends only as high as Z - 30 meters.
2Note the strong peaks in CL which occur at the dew point discontinuities
,
indicating the importance of water vapor in atmospheric stability. In
Fig. 9 we find very low levels of temperature turbulence above the inversion,
2but below the inversion the values of CT are very large considering that
2these are stable conditions. Figs. 10 and 11 show low values of CL, near
2the surface with CL, increasing with height as we approach maximum tempera-
ture at Z =^ 400 meters. In this case, the normal surface layer equations
are a very poor representation. It is also interesting to note that a
nearby profile (Fig. 12, taken about 100 km south of those shown in Figs.
10 and 11) is completely different.
10
V. CONCLUSIONS
In the presence of a raised marine inversion, such as off the Pacific
Coast, a well mixed turbulent boundary layer is usually found. The height
2dependence of C™ in this layer will be well described by the standard
surface layer expressions up to the inversion. In the absence of a strong
raised inversion, such as is often the case off the Atlantic Coast, there
may be no well mixed turbulent boundary layer. This is particularly true
2under stable conditions where the magnitude of CT found at the surface
may in fact be dominated by a low level temperature discontinuity. Under
these conditions, the standard surface layer equations may be invalid above
heights on the order of 10 meters.
Above the boundary layer, air mass boundaries and other sources of
temperature, velocity, and water vapor discontinuities play a critical role
2in the magnitude of CT . This is even more significant for optical propa-
2gation because C,. is also affected by water vapor fluctuations (eq. 1).
A profile taken during FLORIDA 77 (Fig. 13) shows that these layers can
produce large effects as high as 5,000 meters.
ACKNOWLEDGEMENTS
The authors wish to recognize the contributions of Dr. K. L. Davidson ofNPS. Work supported by NAVAIR contract N00019-76-C-0588 and NAVSEA PMS 405
11
REFERENCES
1. Bufton, J.L., Comparison of Vertical profile turbulence structure withstellar observations, Appl . Opt. 12, 1785-1793 (1973).
2. Businger, J. A., J.C. Wyngaard, Y. Izumi and E.F. Bradley, Flux profilerelationships in the atmospheric surface layer, J. Atmos . Sci. 28 ,
181-189 (1971).
3. Collins, S.A., Y.J. Liu and L.E. Pape, Altitude dependence of C^ eval-uation of airborne refractive index fluctuations, Proc. of OpticalPropagation through Turbulence, Rain and Fog, Boulder, CO (1977).
4. Davidson, K.L., T.M. Houlihan, G. Schacher and C.W. Fairall, An exami-nation of scaling laws for Cj^ in the layer adjacent to ocean waves,Proc. of Optical Propagation through Turbulence, Rain and Fog,
Boulder, CO (1977)
.
5. Friehe, Carl A., Estimation of refractive-index temperature structureparameter over the ocean, Appl. Opt. 16 , 334-340 (1977).
6. Hall, Freeman F., Index of refraction structure parameter in the realatmosphere - an overview, Proc. of Optical Propagation throughTurbuelnce, Rain and Fog, Boulder, CO (1977).
7. Hanson, Donald W. , Atmospheric turbulence measurements at AMOS, Proc.of Optical-Submillimeter Atmospheric Propagation Conf
., Colorado
Springs, CO, 245-254 (1976).
8. Hinze, J.D., Turbulence , McGraw-Hill, New York, p 184-204 (1959).
9. Korpov, V.N. and L.R. Tsvang, Characteristics of very small-scale tur-bulence in a stratified boundary layer, Atmos. and Oceanic Phys
.
22_, 1142-1150 (1966).
10. Kraus, E.B., Atmosphere - Oceanic Interaction , Clarendon Press, Oxford,Ch. 5 (1972).
11. Lawrence, R.S., G.R. Ochs and S.F. Clifford, Measurements of atmosphericturbulence relevant to optical propagation, J. Opt. Soc. Am. 60 ,
826-830 (1970).
12. Lumley, J.L. and H.A. Panofsky, The Structure of Atmospheric Turbulence ,
Interscience, New York (1964).
13. Ochs, G.R. and R.S. Lawrence, Temperature and C^ profiles measurementsoverland and ocean to 3 km above the surface, NOAA Technical ReportERL 251-WPL 22 (1972)
.
14. Wyngaard, J.C, Y. Izumi and S.A. Collins, Behavior of the refractive-index-structure parameter near the ground, J. Opt. Soc. Am. 61 ,
1646-1650 (1971)
.
15. Yura, H., Interim Report for ARPA order 2843, SAMOS TR, unpublished.
13
FIGURE CAPTIONS
2 21. Height dependence of C^ /CL, based on eq. 2 for the U.S. Standard
Atmosphere.
22. Height dependence of CT . The solid line is the ground average com-
piled by Hall (1977) for daytime overland profiles. The dashed line
is an extrapolation using eq. 11 from typical shipboard oceanic sur-
face layer measurements.
3. Airborne Research Associates, Inc., Bellanca research aircraft during
operations off Nova Scotia with the USNS Hayes in May of 1977.
24. Wingtip probe configuration for measurement of CT .
25. Height dependence of CL, measured from the Naval Coastal Systems
Laboratory Stage I off Panama City, Florida during FLORIDA 77.
26. Height dependence of C„ for two profiles during CEWCOM 76 with a
simultaneous ship launched radiosonde.
27. Temperature and CT profiles off the New Jersey Coast, 22 Feb. 1977.
The top of the haze layer was 1700 meters.
28. Temperature,dewpoint and C
Tprofile (HAYES 77) near the Nantucket
Light Ship on 16 May 1977 at 1325 ADST.
29. Temperature, dewpoint and C„ profile (HAYES 77) near Cape Sable, N.S
2on 17 May 1977 at 1525 ADST. The x's denote C
Tvalues and the arrow
denotes the ocean temperature measured from the USNS Hayes
.
210. Temperature, dewpoint and C„ profile (HAYES 77) about 20 km east of
Cape Canso, N.S. on 18 May 1977 at 1625 ADST. The x's denote Cp2
values and the arrow denotes the ocean temperature measured from the
USNS Hayes.
15
211. Temperature, dewpoint and (L, profile (HAYES 77) about 20 km east
of Cape Canso, N.S. on 18 May 1977 at 1715 ADST. The x»s denote
2CT values and the arrow denotes the ocean temperature measured from
the USNS Hayes.
212. Temperature, dewpoint and Cp profile (HAYES 77) about 100 km southeast
of Halifax, N.S. on 18 May 1977 at 1750 ADST.
213. Temperature, dewpoint and CL, profile (FLORIDA 77) south of Panama City,
Florida on 19 February 1977 at 1300 CDT. The values of T > T are not
real but represent a calibration shift of the dewpoint instrument.
16
FIGURE 1
r
/
/
/
/
J L_i J I L 1_J I I 1
LO O LO
CVJ
I
SJ>
to
I
2 "J"CM
o
o
£
17
FIGURE 2
10'
10'
n) -
102 -
X\\NN\\N\\X\
j i i nil » i » i i i i 11 l^ i i i i i i i
10-4
C 2(°C
2/m 2/3)
10-3 10 -2
19
21
FIGURE 4
/P- '„„ :
23
10'
FIGURE 5
FLORIDA 77
Z%~TT*
10
1.0 J I l I I I I J L
10" 3
C^(°C^/m 2/3)
10-2
25
FIGURE 6
10
10/5/761625-1632
10/5/761657-1708
10'
Zm)
10
10
C^Z"2/3
10
C?(K 2/m /3)
103
10
(m) 102 -
C?(K2/m2/3)
10-2
T<°n^ 27
FIGURE 7
OX)
'o
ro
•O cm
c:
C\JOo
O
ro
•O
^^'
J L I I I I I I L i i i i i i i
POO*- n e
cvjO
_ O
O
oI
oo
29
FIGURE 8
oCM
£
Oo
CM h-O
oo
05
I I I I I I L I I I i l I I l 1 1 I 1 I I I k_
o *b M CMO
31
FIGURE 9
06
rO
OCM
PH°
oC
\-
_ o
I
i ' 1 1 1 I L
*o
1 1 1l
1 1 L I I I I I I I L
roOcvi
N O
33
FIGURE 10
CM
b
ro
b PO\CM
E
oo
o
b
o
- o
oI
oCO
I
oro
Oo
' ' ' i ii i i_
o ro
o N
'''' I L.
CM
O
35
FIGURE 11
iO
roi
<3-
io
ro
oo
CVJHO
-O
O
-O H
OCM
i
Mill | L I I I i II L Mill I L
o 2> rJ E O
37
FIGURE 12
CVJ
b
b
b
CO
E
oo
CVJHO
h-
h^
'I
l ' I L l I l I I I I i i I i I I L
o
o1
O
H°
oCVJ
i
oro
oro
o N O
39
10 20
C<2,10"3oC
2/ m :
30 -40 -20
t a td,°c
41
INITIAL DISTRIBUTION LIST
No. of Copies
1. Defense Documentation Center 2
Cameron StationAlexandria, Virginia 22314
2. Library, Code 0212 2
Naval Postgraduate SchoolMonterey, California 93940
3. Dean of Research, Code 023 1
Naval Postgraduate SchoolMonterey, California 93940
4. Asst. Professor C. W. Fairall, Code 61Fr 5
Naval Postgraduate SchoolMonterey, California 93940
5. Professor K. E. Woehler, Code 61Wh 1
Naval Postgraduate SchoolMonterey, California 93940
6. Dr. Ralph Markson 5
Airborne Research Associates46 Kendal Common RoadWeston, Massachusetts 02193
7. Assoc. Professor K. L. Davidson, Code 63Ds 1
Naval Postgraduate SchoolMonterey, California 93940
8. Assoc. Professor T. Houlihan, Code 69Hm 1
Naval Postgraduate SchoolMonterey, California 93940
9. Assoc. Professor G. Schacher, Code 61Sq 1
Naval Postgraduate SchoolMonterey, California 93940
10. Mr. Murray Schefer 1
Code Air-3706Naval Air Systems CommandWashington, D.C. 20360
11. LT M. Hughes 1
PM-22/PMS 405
Naval Sea Systems CommandWashington, D.C. 20362
43
12. Dr. Stuart GathamCode 8326Naval Research LaboratoryWashington, D.C. 20375
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